Binary Search Tree: Insertion

March 1, 2023

Insertion in a Binary Search Tree

Binary Search tree is fairly easy and we just need to know a few simple rules given below –

Rules for Insertion in a Binary Search Tree (BST)

The left subtree for any given node will only contain nodes which are lesser than the current node
The right subtree for any given node will only contain nodes which are greater than the current node
Each subtree must also follow the above rules of BST

Pre Requisite to Insertion

Pre-Requisite To insert in Binary search tree we need to search for the correct node where the new node should be insert

So, first, we will learn how to search a given node(value), in a binary search tree

Searching in a Binary Search Tree

Let us say we want to 9 in the binary search tree given in our example above, what approach we would follow?

Algorithm

Start from the root node
Compare the value with the root node, if same then found, return True
If the value is less than the root node, recurse to the left node. Else recurse to the right node
Do this recursively, until the value is found or not found

Example

Assuming we want to find 9 in the above example

The root node is 15, (9 <15) thus recursing to the left node
Now, the left node is 13, (9<14) thus again, recursing to the left node
Now, the left node is 8, (9>8) thus, recursing to the right node
Finally, the right node is 9, (9=9), thus value found, return true

Code to implement Search

// A sample C function to check if a given node exists in a binary search tree or not
struct node* search(struct node* root, int value) 
{ 
    // Check if the root is null or value is present at root itself
    if (root == NULL || root->value == value) 
       return root;

    // Root is smaller than value, go to right subtree's node, doing recusion here
    if (root->value < value) 
       return search(root->right, value); 

    // else only one case is left
    // i.e. Root is greater than value, go to left subtree's node, doing recusion here
    return search(root->left, value); 
}

Priority Queue in C

Tree Traversals: Inorder Postorder Preorder

Inorder Tree Traversal in Binary Tree

Inorder Tree Traversal without Recursion

Preorder Tree Traversal without Recursion

Insertion in a Binary Search Tree

Insertion is fairly simple if you understood search perfectly

Try to search the BST for the node to be inserted
As the node wouldn’t exist we will hit the leaf node, with null as child node right!
Insert the new node here
Voila! Party, you’ve inserted

Code for Binary Search Tree Insertion

Run

// PrepInsta's program to do insertion in a Binary Search Tree (BST)
#include<stdio.h> 
#include<stdlib.h>

// Basic struct of Tree 
struct node 
{ 
    int val; 
    struct node *left, *right; 
}; 
   
// Function to create a new Node
struct node* newNode(int item) 
{ 
    struct node* temp =  (struct node *)malloc(sizeof(struct node)); 
    temp->val = item; 
    temp->left = temp->right = NULL; 
    return temp; 
} 
   
// Function print the node in inorder format, when insertion is complete
void inorder(struct node* root) 
{ 
    if (root != NULL) 
    { 
        inorder(root->left); 
        printf("%d \n", root->val); 
        inorder(root->right); 
    } 
} 
   
// Here we are finding where to insert the new node so BST is followed
struct node* insert(struct node* node, int val) 
{ 
    /* If the tree(subtree) is empty, return a new node by calling newNode func.*/
    if (node == NULL) return newNode(val); 
  
    /* Else, we will do recursion down the tree to further subtrees */
    if (val < node->val) 
        node->left  = insert(node->left, val); 
    else if (val > node->val) 
        node->right = insert(node->right, val);    
  
    /* (Safety) return the node's pointer which is unchanged */
    return node; 
} 
   
int main() 
{ 
    /* Our BST will look like this 
              100 
           /     \ 
          40      140 
         /  \    /  \ 
       40   80  120  160 */
    struct node* root = NULL; 
    root = insert(root, 100); 
    insert(root, 60); 
    insert(root, 40); 
    insert(root, 80); 
    insert(root, 140); 
    insert(root, 120); 
    insert(root, 160);
    
   
    // Finally printing the tree using inorder
    inorder(root); 
   
    return 0; 
}

Output:

How it works?

In binary search trees, we use the INSERT function to add a new element in a tree.
Insertion is similar to searching wherein, we first check if the element is present in the given data or not. If not, the node is entered at that position.
If the data to be added is greater than the parent data node it is inserted towards the right of the parent; else it is inserted to the left of the parent.
In other words,

If root > node,

then the data node is added to the left sub-tree.

If root < node,

then the data node is added to the right sub-tree.

For Example: [15, 18, 13, 8, 14, 4, 16, 19, 9]

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Introduction to Trees

Binary Trees

Binary Tree in Data Structures (Introduction)
Tree Traversals: Inorder Postorder Preorder : C | C++ | Java
Inorder Postorder PreOrder Traversals Examples
- Inorder Tree Traversal in Binary Tree: C | C++ | Java
- Preorder Tree Traversal in Binary Tree : C | C++ | Java
- Postorder Tree Traversal in Binary Tree : C | C++ | Java
Tree Traversal without Recursion
- Postorder Preorder Inorder Traversal without recursion
- Inorder Tree Traversal without Recursion – C | C++ | Java
- Preorder Tree Traversal without Recursion – C | C++ | Java
- Postorder Tree Traversal without Recursion – C | C++ | Java

Binary Search Trees

Binary search tree in Data Structures (Introduction)
- BST: Introduction to Binary Search Tree
- BST: Binary Search Tree Program : C | C++ | Java
- BST: Search a node in Binary Search Tree : C | C++ | Java
- BST: Insertion in a Binary Search Tree : C | C++ | Java
- BST: Deletion in a Binary Search Tree : C | C++ | Java

Traversals

Traversal in Trees
Tree Traversals: Breadth-First Search (BFS) : C | C++ | Java
Tree Traversals: Depth First Search (DFS) : C | C++ | Java
Construct a Binary Tree from Postorder and Inorder

B – Trees

B-Tree
- B-Tree: Introduction
- B-Tree: Insertion : C | C++ | Java
- B-Tree: Deletion : C | C++ | Java

AVL Trees

AVL Trees
- AVL Trees: Introduction
- AVL Tree Insertion : C | C++ | Java
- AVL Tree Deletion : C | C++ | Java
- Insertion in a Binary Tree (Level Order) – C | C++ | Java
- Searching in Binary Tree – C | C++ | Java
- Searching in a Binary Search Tree – C | C++ | Java

Complete Programs for Trees

Depth First Traversals – C | C++ | Java
Level Order Traversal – C | C++ | Java
Construct Tree from given Inorder and Preorder traversals – C | C++ | Java
Construct Tree from given Postorder and Inorder traversals – C | C++ | Java
Construct Tree from given Postorder and Preorder traversal – C | C++ | Java
Find size of the Binary tree – C | C++ | Java
Find the height of binary tree – C | C++ | Java
Find maximum in binary tree – C | C++ | Java
Check whether two tree are identical- C| C++| Java
Spiral Order traversal of Tree- C | C++| Java
Level Order Traversal Line by Line – C | C++| Java
Hand shaking lemma and some Impotant Tree Properties.
Check If binary tree if Foldable or not.- C| C++| Java
check whether tree is Symmetric – C| C++| Java.
Check for Children-Sum in Binary Tree- C|C++| Java
Sum of all nodes in Binary Tree- C | C++ | Java
Lowest Common Ancestor in Binary Tree- C | C++ | Java